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A287797
Triangle read by rows: T(n,k) gives the independence number of the k X n knight graph.
0
1, 2, 4, 3, 4, 5, 4, 4, 6, 8, 5, 6, 8, 10, 13, 6, 8, 9, 12, 15, 18, 7, 8, 11, 14, 18, 21, 25, 8, 8, 12, 16, 20, 24, 28, 32, 9, 10, 14, 18, 23, 27, 32, 36, 41, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50, 11, 12, 17, 22, 28, 33, 39, 44, 50, 55, 61
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Independence Number
Eric Weisstein's World of Mathematics, Knight Graph
FORMULA
T(n,n) = A030978(n).
T(n,2) = A201629(n+1).
EXAMPLE
1;
2, 4;
3, 4, 5;
4, 4, 6, 8;
5, 6, 8, 10, 13;
6, 8, 9, 12, 15, 18;
MATHEMATICA
Table[IndependenceNumber[KnightTourGraph[m, n]], {n, 10}, {m, n}] // Flatten
Table[Piecewise[{{Max[m, n], Min[m, n] == 1}, {Max[m, n] + 1, Min[m, n] == 2 && Mod[Max[m, n], 2] == 1}, {4 Round[(Max[m, n] + 1)/4], Min[m, n] == 2 && Mod[Max[m, n], 2] == 0}, {m n/2, Mod[m n, 2] == 0}, {(m n + 1)/2, Mod[m n, 2] == 1}}], {n, 10}, {m, n}] // Flatten
CROSSREFS
Cf. A030978 (n X n knight graphs).
Cf. A201629 (2 X n knight graphs).
Sequence in context: A274047 A226644 A083172 * A369430 A360691 A302707
KEYWORD
nonn,tabl
AUTHOR
Eric W. Weisstein, Jun 01 2017
STATUS
approved